Stochastic Averaging and Extremum Seeking treats methods inspired by
attempts to understand the seemingly non-mathematical question of
bacterial chemotaxis and their application in other environments. The
text presents significant generalizations on existing stochastic
averaging theory developed from scratch and necessitated by the need to
avoid violation of previous theoretical assumptions by algorithms which
are otherwise effective in treating these systems. Coverage is given to
four main topics.
Stochastic averaging theorems are developed for the analysis of
continuous-time nonlinear systems with random forcing, removing prior
restrictions on nonlinearity growth and on the finiteness of the time
interval. The new stochastic averaging theorems are usable not only as
approximation tools but also for providing stability guarantees.
Stochastic extremum-seeking algorithms are introduced for optimization
of systems without available models. Both gradient- and Newton-based
algorithms are presented, offering the user the choice between the
simplicity of implementation (gradient) and the ability to achieve a
known, arbitrary convergence rate (Newton).
The design of algorithms for non-cooperative/adversarial games is
described. The analysis of their convergence to Nash equilibria is
provided. The algorithms are illustrated on models of economic
competition and on problems of the deployment of teams of robotic
vehicles.
Bacterial locomotion, such as chemotaxis in E. coli, is explored with
the aim of identifying two simple feedback laws for climbing nutrient
gradients. Stochastic extremum seeking is shown to be a
biologically-plausible interpretation for chemotaxis. For the same
chemotaxis-inspired stochastic feedback laws, the book also provides a
detailed analysis of convergence for models of nonholonomic robotic
vehicles operating in GPS-denied environments.
The book contains block diagrams and several simulation examples,
including examples arising from bacterial locomotion, multi-agent
robotic systems, and economic market models.
Stochastic Averaging and Extremum Seeking will be informative for
control engineers from backgrounds in electrical, mechanical, chemical
and aerospace engineering and to applied mathematicians. Economics
researchers, biologists, biophysicists and roboticists will find the
applications examples instructive.
